The Great Western/Downtown Tulsa Hotel is undergoing substantial renovation so I can't give any guidance until that's completed. The Crowne Plaza is also completing renovations (downtown Tulsa is renovating substantially as the completion date for the new BOK Center approaches) so I can't give any guidance about it, either.
The Doubletree Downtown is OK; Doubletree South is even nicer (61st & Yale).
If price is not a concern, the Ambassador Hotel is probably the nicest hotel in the downtown area. Website: www.hotelambassador-tulsa.com.
Downtown Tulsa is a pretty safe neighborhood. Other than the occasional panhandler (and I get panhandled less than 1x/month--and I work downtown and live a mile south of downtown), I have no concerns about safety there despite the concentration of services for the homeless provided by various charities just North of the main downtown area.